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Use long division, define each quotient
(3x^2- 3x + 5) ÷ (x - 6)

User Sahaj
by
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1 Answer

3 votes

Answer:

(x - 6)(3x + 15) + 95

Explanation:

Here's the long division of (3x^2 - 3x + 5) ÷ (x - 6):

3x + 15

--------------

x - 6 | 3x^2 - 3x + 5

- (3x^2 - 18x)

--------------

15x + 5

- (15x - 90)

------------

95

Therefore, the quotient is 3x + 15, and the remainder is 95.

The quotient represents the result of the division of the polynomial (3x^2 - 3x + 5) by the divisor (x - 6). In particular, the quotient 3x + 15 represents the linear polynomial that, when multiplied by the divisor x - 6, gives the dividend 3x^2 - 3x + 5.

In other words, we have:

(3x^2 - 3x + 5) = (x - 6)(3x + 15) + 95

The remainder 95 indicates that the division is not exact, and that there is a "leftover" term of 95 when we try to divide the polynomial (3x^2 - 3x + 5) by (x - 6).

User Rlpowell
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7.1k points